4. Show that the internal energy, U, of an Einstein crystal is given by: 3Nhv 3Nhv exp(-ẞhv) U 2 1-exp(-ẞhv) Hint: The following identity will avoid you having to use the chain rule: f(x) -(f'(x))e" d In(1-x)) = f(x) dx 1-e

Chemistry: Principles and Practice
3rd Edition
ISBN:9780534420123
Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Publisher:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Chapter5: Thermochemistry
Section: Chapter Questions
Problem 5.26QE
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thermodynamics

4. Show that the internal energy, U, of an Einstein crystal is given by:
3Nhv 3Nhv exp(-ẞhv)
U
2
1-exp(-ẞhv)
Hint: The following identity will avoid you having to use the chain rule:
f(x)
-(f'(x))e"
d
In(1-x)) =
f(x)
dx
1-e
Transcribed Image Text:4. Show that the internal energy, U, of an Einstein crystal is given by: 3Nhv 3Nhv exp(-ẞhv) U 2 1-exp(-ẞhv) Hint: The following identity will avoid you having to use the chain rule: f(x) -(f'(x))e" d In(1-x)) = f(x) dx 1-e
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